基于高阶位移场理论的多孔金属圆柱壳结构响应研究

Research on Structural Response of Metallic Lattice Tube Based on Higher-Order Field Displacement ( HOFD) Theory

基于高阶位移场理论研究了简支条件棱镜型圆柱壳体在内压力作用下的结构响应。首先,建立承受内压圆柱壳体的平衡方程,计算在该载荷作用下的各项同性材料的响应,与弹性力学理论解进行对比,验证所得平衡方程的正确性。采用均匀化方法,将正方形,三角形和Kagome 3种多孔金属圆柱壳体等效为正交各向异性的材料,计算了在内压下的结构响应,并与有限元计算结果进行对比,结果表明文中方法所得结果与有限元的结果非常接近,计算得到的径向位移和轴向应变与有限元的计算基本相同,径向应力,环向应力和径向应变等结构响应时误差也较小。3种构型的计算结果与有限元计算结果的比值变化趋势基本相同,其中三角形和Kagome构型的计算结果较正方形构型的计算结果较为准确。通过对所得结果进行分析,可以发现该高阶位移场理论在计算圆柱壳体结构响应时有效、准确,可以作为预测该类结构响应的计算方法。

A metallic cylindrical lattice tube under internal pressure was analyzed by using the HODF theory. The response of the structure was obtained and compared with that obtained by using the FEM analysis. By using the homogenization method, three cylindrical lattice tubs, whose lattice types were Triangle, Square, and Kagome re- spectively, under internal pressure were homogenized to be orthotropic material and calculated by HODF theory. The HODF theoretical results and the FEM results were respectively obtained and their comparisons show that the differences are very small. The radial displacement and axial displacement obtained with HODF theory are nearly the same as the respective displacements obtained with FEM. The errors in radial stress, hoop stress and radial strain are relatively small. The ratios of the displacements obtained respectively with HODF theory and FEM are calculated and the patterns of these respective ratios are nearly the same. The results of Triangle and Kagome are better than the results of Square. The comparison and analysis of calculated results confirm preliminarily that the higher-order displacement theory can be used to calculate the correct responses of the metallic cylindrical lattice tube under internal pressure.